In this work, mass attenuation coefficients (mu/rho), effective atomic number (Z(eff)), electron density (N-e), mean free path (MFP), and half-value layer (HVL) of 20 BaO/SrO-(x) Bi2O3-(80-x) B2O3 glasses (where x = 10, 20, 30, 40, 50 and 60 mol%) were calculated using WinXCom program and MCNP5 code. The obtained (mu/rho) results using both MCNP5 code and WinXCom program were in good agreement. It is found that the addition of Bi2O3 leads to increase the Z(eff) values in both BaO/SrO-Bi2O3-B2O3 glass systems. However, the Z(eff) values of the BaO-Bi2O3-B2O3 glass system are higher than those of the SrO-Bi2O3-B2O3 glasses. The fast neutrons effective removal cross sections (Sigma(R)) for 20 SrO-40 Bi2O3-40 B2O3 glass is the highest among all studied glasses. The calculated half-value layer values were compared with different glass systems and it was found that the shielding properties of the selected glasses are comparable or even better than other glass systems such as phosphate glasses.